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Operational Geometry of Noise in Superconducting Processors

Smiljko Kajtez

Published May 15, 2026• 0 citations
Publisher

Abstract

Accurate modeling of noise is a central challenge for scaling superconducting quantum hardware. Standardapproaches typically assume stationary, memoryless and gate-local noise. On current processors with morethan one hundred qubits, these approximations break down: we observe short-term drift, history dependence,device-wide fluctuations and non-monotonic idle behavior.We introduce an operational measure of two-qubit noise, the information distance di j(t) = −lnFi j(t), defineddirectly from GHZ2 fidelities. This quantity is empirical and time dependent. Crucially, it does not followphysical distance on the hardware graph: adjacent qubits can have large di j, while multi-hop connections canhave smaller di j. The resulting “noise geometry” is induced by information flow rather than physical layout.Using more than 50 000 circuits across three IBM heavy-hex processors (Marrakesh, Fez and Torino), weobserve usage-dependent changes of 0.002–0.02 in di j, minute-scale relaxation, slower device-wide drift andnon-monotonic idle-time distinguishability. These local variations accumulate along multi-qubit paths. Onibm marrakesh, a trained seven-qubit path outperforms a baseline GHZ7 circuit in all 20 interleaved trials,with a mean fidelity gain of 1.6×10−2and reduced variance.We summarize these observations with a minimal dynamical model in which information distances evolve under usage, relaxation, local fluctuations and a global drift process. The results indicate that noise on present-daysuperconducting processors is time dependent, history dependent and structured in a way that is not captured bystatic gate-local models, and that operational information distance provides a practical geometry for describingthis structure.

DOI
10.5281/zenodo.20213286

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Accurate modeling of noise is a central challenge for scaling superconducting quantum hardware. Standardapproaches typically assume stationary, memoryless and gate-local noise. On current processors with morethan one hundred qubits, these approximations break down: we observe short-term drift, history dependence,device-wide fluctuations and non-monotonic idle behavior.We introduce an operational measure of two-qubit noise, the information distance di j(t) = −lnFi j(t), defineddirectly from GHZ2 fidelities. This quantity is empirical and time dependent. Crucially, it does not followphysical distance on the hardware graph: adjacent qubits can have large di j, while multi-hop connections canhave smaller di j. The resulting “noise geometry” is induced by information flow rather than physical layout.Using more than 50 000 circuits across three IBM heavy-hex processors (Marrakesh, Fez and Torino), weobserve usage-dependent changes of 0.002–0.02 in di j, minute-scale relaxation, slower device-wide drift andnon-monotonic idle-time distinguishability. These local variations accumulate along multi-qubit paths. Onibm marrakesh, a trained seven-qubit path outperforms a baseline GHZ7 circuit in all 20 interleaved trials,with a mean fidelity gain of 1.6×10−2and reduced variance.We summarize these observations with a minimal dynamical model in which information distances evolve under usage, relaxation, local fluctuations and a global drift process. The results indicate that noise on present-daysuperconducting processors is time dependent, history dependent and structured in a way that is not captured bystatic gate-local models, and that operational information distance provides a practical geometry for describingthis structure.
The influence of noise on quantum dynamics is one of the main factors preventing current quantum processors from performing accurate quantum computations. Sufficient noise characterization and modeling can provide key insights into the effect of noise on quantum algorithms and inform the design of targeted error protection protocols. However, constructing effective noise models that are sparse in model parameters, yet predictive can be challenging. In this work, we present an approach for effective noise modeling of multi-qubit operations on transmon-based devices. Through a comprehensive characterization of seven devices offered by the IBM Quantum Platform, we show that the model can capture and predict a wide range of single- and two-qubit behaviors, including non-Markovian effects resulting from spatiotemporally correlated noise sources. The model’s predictive power is further highlighted through multi-qubit dynamical decoupling demonstrations and an implementation of the variational quantum eigensolver. As a training proxy for the hardware, we show that the model can predict expectation values within a relative error of 0.5%; this is a sevenfold improvement over default hardware noise models. Through these demonstrations, we highlight key error sources in superconducting qubits and illustrate the utility of reduced noise models for predicting hardware dynamics.
Quantum computing holds the promise of transforming computational paradigms across science and engineering. But realizing potential on near term hardware demands on understanding of the noise processes that corrupt quantum circuit outputs. On superconducting processors, fragile qubits are continuously subjected to environmental disturbances including T1T_1T1​ relaxation, charge noise, and magnetic flux drift that cause measurement statistics to evolve in a nonstationary manner across repeated circuit executions, undermining the reliability of any result aggregated over a long experimental session. In this work, we treat the sequence of bitstring count outcomes from repeated executions of a fixed quantum circuit as a time series and conduct a systematic statistical investigation of its structure. The first contribution is constructing a predictive model of circuit output, demonstrating that future measurement outcomes can be forecast by exploiting temporal correlations in the execution record. We then extend the analysis to two circuits sharing the same physical qubit, examining cross-series dependencies and evaluating whether the drift behavior of one circuit can inform predictions about the other. The temporal structure of the signals is characterized in depth. The other contribution of this dissertation is to perform Wavelet-based multifractal analysis to reveal that quantum circuit outputs exhibit genuine multifractality. This is a hallmark of long range correlated, scale free processes rather than the simple Gaussian white noise assumed by standard error models. Complementary frequency-domain analysis identifies a residual 1/f1/f1/f noise component that persists after linear detrending, consistent with charge and flux noise mechanisms well documented in superconducting qubit literature. Motivated by these findings, The other contribution is to design and evaluate a suite of drift-mitigation filters including piecewise Huber regression, rolling median, smoothing spline, and Savitzky–Golay approaches under a rigorous chronological train/test protocol that mimics real operational deployment. The smoothing spline and median filter achieve near-zero corrected bias, while the rolling median emerges as the preferred solution for online, shot-by-shot correction due to its causal update structure and maximal robustness to impulsive hardware events. Taken together, our results characterize quantum circuit outputs as non-stationary, multifractal processes exhibiting long memory, seasonality, and inter-circuit causality, and establish a principled filtering framework for mitigating temporal bias drift in NISQ era quantum hardware.
Qubit layout selection determining which physical qubits a logical circuit occupies on a superconducting processor is fundamentally a noise-field sampling problem. On IBM Heron r1 and Heron r2 devices, two-qubit gate error varies by nearly one order of magnitude (7– $9\times $ ) across qubit pairs on the same chip, causing measured fidelity differences up to 0.903 from layout choice alone. We introduce the Gate Noise Sensitivity Index (GNSI), a calibration-weighted linear combination of per-qubit readout error and per-edge two-qubit gate error, derived analytically as a first-order approximation of circuit fidelity under independent, heterogeneous noise channels. For 12 backend–circuit combinations on three IBM processors (133-qubit Heron r1 and 156-qubit Heron r2), GNSI scores are computed for the full pool of 1,320 computationally enumerated candidate layouts; the top-ranked (GNSI-BEST) and bottom-ranked (GNSI-WORST) layouts are then executed on hardware. GNSI-BEST ranks first by score in all 12 instances (Hit@1 = 100% within the enumerated candidate pool) and consistently achieves higher measured fidelity than GNSI-WORST, with Spearman rank correlation ρ=0.926±0.016\rho = 0.926 \pm 0.016ρ=0.926±0.016 and statistically significant fidelity separation in 9 of 12 paired tests. Initial hardware comparisons on ibm_fez ( n=5n=5n=5 ) show GNSI-BEST matching or exceeding SABRE-selected fidelity. We further identify a depth-dependent regime transition: gate-error heterogeneity appears to govern ranking in shallow circuits (depth ≤15\leq 15≤15 ), while qubit-specific T1T_{1}T1​ variation may dominate for deeper circuits (depth ≥20\geq 20≥20 ). The analytic regime boundary d∗(b)d^{*}(b)d∗(b) , computable from calibration data alone, shows agreement within ±2 depth layers across all three backends in initial comparisons; GNSI-Extended incorporating the decoherence term receives an initial hardware comparison on two circuits, with full validation left to future work. These results suggest that layout-dependent fidelity variation may be governed by a calibration-predictable noise field, with direct implications for compiler design and noise-adaptive quantum circuit execution.
Non-Markovian noise can be a significant source of errors in superconducting qubits. We develop gate sequences utilising mirrored pseudoidentities that allow us to characterise and model the effects of non-Markovian noise on both idle and driven qubits. We compare three approaches to modelling the observed noise: (i) a Markovian noise model, (ii) a model including interactions with a two-level system (TLS), (iii) a model utilising the post Markovian master equation (PMME), which we show to be equivalent to the qubit-TLS model in certain regimes. When running our noise characterisation circuits on a superconducting qubit device we find that purely Markovian noise models cannot reproduce the experimental data. Our model based on a qubit-TLS interaction, on the other hand, is able to closely capture the observed experimental behaviour for both idle and driven qubits. We investigate the stability of the noise properties of the hardware over time, and find that the parameter governing the qubit-TLS interaction strength fluctuates significantly even over short time-scales of a few minutes. Finally, we evaluate the changes in the noise parameters when increasing the qubit drive pulse amplitude. We find that although the hardware noise parameters fluctuate significantly over different days, their drive pulse induced relative variation is rather well defined within computed uncertainties: both the phase error and the qubit-TLS interaction strength change significantly with the pulse strength, with the phase error changing quadratically with the amplitude of the applied pulse. Since our noise model can closely describe the behaviour of idle and driven qubits, it is ideally suited to be used in the development of quantum error mitigation and correction methods.
Quantum computers are capable of carrying out calculations that are challenging or even impossible for classical computers. Quantum computers consist of quantum bits (qubits) which can exhibit a phenomenon called superposition where the qubit is in multiple states at the same time. Qubits can also be entangled with other qubits, which means that the states of the qubits are dependant on each other in a way that the state of a single qubit can not be expressed independently of the other qubits. These properties of qubits that enable quantum computing, are very sensitive to perturbations a ecting the system of qubits from the outside. A common choice for the physical architecture of a qubit is a superconducting qubit, which has its quantum properties implemented with a superconducting circuit. Realising a su ciently large qubit system has remained a challenge, since increasing the size of the system leads to more unwanted noise that interacts with the qubits. We have only just achieved systems that can outperform classical computers in speci c tasks. These devices do not o er signi cant advantages and the goal remains to grow the qubit systems, and overcoming the challenges caused by noise is of high importance. The e ect of noise can be reduced by designing hardware that has minimal sources of noise, or by creating qubits with error correction, meaning a way of undoing the e ect of noise on a qubit. Both of these approaches demand a way of recognising the noise mechanisms and their signi cance. Noise characterisation can be done with combining a theoretical model for the dynamics of a qubit with measurement data obtained from the qubit system in question. A su cient t of a theoretical model to noisy measurement data provides parametrisation of the noise, and a well designed model can link the noise to real physical phenomena. In this work, we introduce a noise model based on the Non-Markovian Quantum State Di usion equation. We present the physical processes the model describes and showcase its performance with noisy measurement data obtained with a real quantum processor consisting of superconducting qubits.
Accurate noise characterization is essential for scaling quantum processors toward fault-tolerant operation. Although reduced qubit dynamics are often modeled with Markovian master equations, present-day devices can exhibit memory effects generated by residual qubit-qubit couplings, structured environments, and finite bath correlation times. Here we develop a channel-resolved, Post-Markovian Master Equation model for non-Markovian noise and test it in superconducting qubits. Using idle-evolution tomography on IBM Quantum processors, we identify complementary operational signatures of non-Markovianity, including violations of CP-divisibility and revivals of distinguishability-based information-backflow measures. We further derive a closed-form spectator-ZZZZZZ model with local dissipation and show that it captures the observed transverse Bloch-vector revivals while leaving the longitudinal relaxation mode Markovian within the model. The fitted closed-form dynamics enable an analytical reconstruction of the transverse memory kernel, whose damped oscillatory structure captures the non-Markovian correction beyond the fitted Markovian baseline. Two-qubit tomography shows buildup and revivals of quantum mutual information on comparable timescales, supporting spectator-induced crosstalk as an important contributor to the observed memory effects. Our results connect operational non-Markovianity diagnostics, microscopic crosstalk modeling, and reduced memory-kernel reconstruction in a single experimental framework for superconducting quantum hardware.